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Abstract Algebra

Abstract Algebra - 3rd edition

ISBN13: 978-0471433347

Cover of Abstract Algebra 3RD 04 (ISBN 978-0471433347)
ISBN13: 978-0471433347
ISBN10: 0471433349
Cover type:
Edition/Copyright: 3RD 04
Publisher: John Wiley & Sons, Inc.
Published: 2004
International: No
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Abstract Algebra - 3RD 04 edition

ISBN13: 978-0471433347

David S. Dummit and Richard M. Foote

ISBN13: 978-0471433347
ISBN10: 0471433349
Cover type:
Edition/Copyright: 3RD 04
Publisher: John Wiley & Sons, Inc.

Published: 2004
International: No
Summary

Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.

Table of Contents

Preface.
Preliminaries.

PART I: GROUP THEORY.

Chapter 1. Introduction to Groups.
Chapter 2. Subgroups.
Chapter 3. Quotient Group and Homomorphisms.
Chapter 4. Group Actions.
Chapter 5. Direct and Semidirect Products and Abelian Groups.
Chapter 6. Further Topics in Group Theory.

PART II: RING THEORY.

Chapter 7. Introduction to Rings.
Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.
Chapter 9. Polynomial Rings.

PART III: MODULES AND VECTOR SPACES.

Chapter 10. Introduction to Module Theory.
Chapter 11. Vector Spaces.
Chapter 12. Modules over Principal Ideal Domains.

PART IV: FIELD THEORY AND GALOIS THEORY.

Chapter 13. Field Theory.
Chapter 14. Galois Theory.

PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND
HOMOLOGICAL ALGEBRA.

Chapter 15. Commutative Rings and Algebraic Geometry.
Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.
Chapter 17. Introduction to Homological Algebra and Group Cohomology.

PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS.

Chapter 18. Representation Theory and Character Theory.
Chapter 19. Examples and Applications of Character Theory.


Appendix I: Cartesian Products and Zorn's Lemma.
Appendix II: Category Theory.
Index.

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